Visible-Infrared person re-identification (VI-ReID) is an important and challenging task in intelligent video surveillance. Existing methods mainly focus on learning a shared feature space to reduce the modality discrepancy between visible and infrared modalities, which still leave two problems underexplored: information redundancy and modality complementarity. To this end, properly eliminating the identity-irrelevant information as well as making up for the modality-specific information are critical and remains a challenging endeavor. To tackle the above problems, we present a novel mutual information and modality consensus network, namely CMInfoNet, to extract modality-invariant identity features with the most representative information and reduce the redundancies. The key insight of our method is to find an optimal representation to capture more identity-relevant information and compress the irrelevant parts by optimizing a mutual information bottleneck trade-off. Besides, we propose an automatically search strategy to find the most prominent parts that identify the pedestrians. To eliminate the cross- and intra-modality variations, we also devise a modality consensus module to align the visible and infrared modalities for task-specific guidance. Moreover, the global-local feature representations can also be acquired for key parts discrimination. Experimental results on four benchmarks, i.e., SYSU-MM01, RegDB, Occluded-DukeMTMC, Occluded-REID, Partial-REID and Partial\_iLIDS dataset, have demonstrated the effectiveness of CMInfoNet.